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Strong Reduction of Combinatory Calculus with Streams

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Abstract

This paper gives the strong reduction of the combinatory calculus SCL, which was introduced as a combinatory calculus corresponding to the untyped Lambda-mu calculus. It proves the confluence of the strong reduction. By the confluence, it also proves the conservativity of the extensional equality of SCL over the combinatory calculus CL, and the consistency of SCL.

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References

  1. David R.: direct proof of the confluence of combinatory strong reduction. Theoretical Computer Science 410(42), 4204–4215 (2009)

    Article  Google Scholar 

  2. Dehornoy, P. and V. van Oostrom, Z, proving confluence by monotonic single-step upperbound functions, in Logical Models of Reasoning and Computation (LMRC-08), 2008. Slides available on http://www.phil.uu.nl/oostrom/publication/talk/lmrc060508.pdf.

  3. Hindley R., Seldin J.P.: Lambda-Calculus and Combinators, an Introduction. Cambridge University Press, Cambridge (2008)

    Book  Google Scholar 

  4. Komori Y., Matsuda N., Yamakawa F.: A simplified proof of the church-rosser theorem. Studia Logica 102(1), 175–183 (2013)

    Article  Google Scholar 

  5. Minari P.: A solution to curry and hindley’s problem on combinatory strong reduction. Archive for Mathematical Logic 48(2), 159–184 (2009)

    Article  Google Scholar 

  6. Nakazawa, K. and S. Katsumata, Extensional models of untyped Lambda-mu calculus, in Fourth International Workshop on Classical Logic and Computation (CL&C’12), vol. 97 of Electric Proceedings in Theoretical Computer Science, pp. 35–47, 2012.

  7. Parigot, M., λμ-Calculus: an algorithmic interpretation of classical natural deduction, in Proceedings of the International Conference on Logic Programming and Automated Reasoning (LPAR ’92), vol. 624 of Lecture Notes in Computer Science. Springer, Berlin, 1992, pp. 190–201.

  8. Saurin, A., Separation with streams in the Λμ-calculus, in 20th Annual IEEE Symposium on Logic in Computer Science (LICS’ 05). IEEE Computer Society, New York, 2005, pp. 356–365.

  9. Saurin, A. Standardization and Böhm trees for Λμ-calculus, in Tenth International Symposium on Functional and Logic Programming (FLOPS 2010), vol. 6009 of Lecture Notes in Computer Science. Springer, 2010, pp. 134–149.

  10. Saurin A.: Typing streams in the Λμ-calculus. ACM Transactions on Computational Logic 11, 1–34 (2010)

    Article  Google Scholar 

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Authors and Affiliations

  1. Graduate School of Informatics, Kyoto University, Kyoto, Japan

    Koji Nakazawa

  2. FORCIA, Inc., Tokyo, Japan

    Hiroto Naya

Authors
  1. Koji Nakazawa
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  2. Hiroto Naya
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Correspondence to Koji Nakazawa.

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Presented by Daniele Mundici

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Nakazawa, K., Naya, H. Strong Reduction of Combinatory Calculus with Streams. Stud Logica 103, 375–387 (2015). https://doi.org/10.1007/s11225-014-9570-3

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  • DOI: https://doi.org/10.1007/s11225-014-9570-3

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